Abstract

A formalism for analyzing the complete set of field equations describing macroscopic gravity is presented. Using this formalism, a cosmological solution to the macroscopic gravity equations is determined. It is found that if a particular segment of the connection correlation tensor is zero and if the macroscopic geometry is described by a flat Robertson–Walker metric, then the effective correction to the averaged Einstein field equations of general relativity i.e., the backreaction, is equivalent to a positive spatial curvature term. This investigation completes the analysis of Coley et al. [Phys. Rev. Lett.95, 151102 (2005)], and the formalism developed provides a possible basis for future studies.

Received 22 May 2009Accepted 10 July 2009Published online 25 August 2009

Acknowledgments:

This research was supported by St. Francis Xavier University’s Council on Research, funding from the W.F. James Chair, and an NSERC Discovery Grant. The author wishes to acknowledge the contributions of Dr. Roustam Zalaletdinov who guided the preliminary stages of this research during his stay at St. Francis Xavier University as the W.F. James Chair in Pure and Applied Science. The author would also like to thank Dr. Nicos Pelavas for his technical advice.

Article outline:I. THE AVERAGING PROBLEM IN COSMOLOGYII. THE FIELD EQUATIONS OF MACROSCOPIC GRAVITYA. Brief review of macroscopic gravityB. Timelike vectors and projectionsC. The field equations for the connection correlation tensor1. Algebraic cyclic identities2. Equiaffinity constraint3. Differential cyclic constraint4. The quadratic constraintD. The field equations for the affine deformation tensorE. The averaged Einstein tield equationsIII. MACROSCOPIC GRAVITY IN A FLAT SPATIALLY HOMOGENEOUS AND ISOTROPIC SPACE-TIMEA. AssumptionsB. The connection correlation tensor1. Equivalence classes2. VariablesC. The field equations for the connection correlation tensorD. The field equations for the affine deformation tensorE. The averaged Einstein field equationsIV. CONCLUSIONS